A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:
- The left subtree of a node contains only nodes with keys less than or equal to the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- Both the left and right subtrees must also be binary search trees.
Insert a sequence of numbers into an initially empty binary search tree. Then you are supposed to count the total number of nodes in the lowest 2 levels of the resulting tree.
Input Specification:
Each input file contains one test case. For each case, the first line gives a positive integer N (≤) which is the size of the input sequence. Then given in the next line are the N integers in [which are supposed to be inserted into an initially empty binary search tree.
Output Specification:
For each case, print in one line the numbers of nodes in the lowest 2 levels of the resulting tree in the format:
n1 + n2 = n
where n1 is the number of nodes in the lowest level, n2 is that of the level above, and n is the sum.
Sample Input:
9
25 30 42 16 20 20 35 -5 28
Sample Output:
2 + 4 = 6
1 #include <iostream> 2 #include <queue> 3 #include <vector> 4 using namespace std; 5 struct Node 6 { 7 int v; 8 Node *l, *r; 9 Node(int a = -1) :v(a), l(nullptr), r(nullptr) {} 10 }; 11 Node* root = nullptr; 12 int n, level = -1, a; 13 vector<int>res; 14 void creatTree(Node*& root, int x) 15 { 16 if (root == nullptr) 17 { 18 root = new Node(x); 19 return; 20 } 21 if (x <= root->v) 22 creatTree(root->l, x); 23 else 24 creatTree(root->r, x); 25 } 26 void BFS(Node* root) 27 { 28 queue<Node*>q; 29 q.push(root); 30 while (!q.empty()) 31 { 32 int num = 0; 33 queue<Node*>temp; 34 while (!q.empty()) 35 { 36 Node* p = q.front(); 37 q.pop(); 38 num++; 39 if (p->l != nullptr) 40 temp.push(p->l); 41 if (p->r != nullptr) 42 temp.push(p->r); 43 } 44 q = temp; 45 res.push_back(num); 46 } 47 } 48 int main() 49 { 50 51 cin >> n; 52 while (n--) 53 { 54 cin >> a; 55 creatTree(root, a); 56 } 57 BFS(root); 58 cout << res[res.size() - 1] << " + " << res[res.size() - 2] << " = " << res[res.size() - 1] + res[res.size() - 2] << endl; 59 return 0; 60 }